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Towards Understanding Theoretical Advantages of Complex-Reaction Networks
- Source :
- Neural Networks,151: 80-93. 2022
- Publication Year :
- 2021
-
Abstract
- Complex-valued neural networks have attracted increasing attention in recent years, while it remains open on the advantages of complex-valued neural networks in comparison with real-valued networks. This work takes one step on this direction by introducing the \emph{complex-reaction network} with fully-connected feed-forward architecture. We prove the universal approximation property for complex-reaction networks, and show that a class of radial functions can be approximated by a complex-reaction network using the polynomial number of parameters, whereas real-valued networks need at least exponential parameters to reach the same approximation level. For empirical risk minimization, our theoretical result shows that the critical point set of complex-reaction networks is a proper subset of that of real-valued networks, which may show some insights on finding the optimal solutions more easily for complex-reaction networks.
- Subjects :
- Computer Science - Machine Learning
Computer Science - Artificial Intelligence
Subjects
Details
- Database :
- arXiv
- Journal :
- Neural Networks,151: 80-93. 2022
- Publication Type :
- Report
- Accession number :
- edsarx.2108.06711
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1016/j.neunet.2022.03.024